A big thanks to everyone for your responses - has to be the first time this week I've prompted discussion on 19th century legislation

The Baptism record I have is a legitimate transcription (made in 1919) from the original parish registers. I'm based in Australia, but when I finally make it to London (the place of birth) I'll try to view the original with my own eyes.
I've looked a bit closer at the birth certificate, and it appears the informant wasn't either of the parents, but one of the next-door neighbours who was listed as "present at birth" (strange by today's standards, but times change). I suppose it could be that she remembered the birth was on a particular day of the week but miscalculated how long ago it was. Some things are just lost in time, though.
As the baptism record is closer to the DOB, whatever it may be, and would have had the parents present, I am finding it more convincing (will still list both dates though). I don't think that there was any WWI service but I'll ask my dad. Barring that, I'll check the newspapers for a birth notice.
Thanks once again for all of your ideas.